The inverse along an element in rings with an involution, Banach algebras and -algebras

DOI10.1080/03081087.2016.1183559zbMath1361.15004arXiv1509.04251OpenAlexW2262982249MaRDI QIDQ2961470

Enrico Boasso, Julio Benítez Lopez

Publication date: 20 February 2017

Published in: Linear and Multilinear Algebra (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1509.04251

zbMATH Keywords

Banach algebra\(C^*\)-algebraDrazin inverseMoore-Penrose inversegroup inverseinvertibility along an elementring with an involution

Mathematics Subject Classification ID

Theory of matrix inversion and generalized inverses (15A09) Selfadjoint operator algebras ((C^*)-algebras, von Neumann ((W^*)-) algebras, etc.) (46L99) Rings with involution; Lie, Jordan and other nonassociative structures (16W10) General (adjoints, conjugates, products, inverses, domains, ranges, etc.) (47A05) Topological algebras, normed rings and algebras, Banach algebras (46H99)

Related Items (14)

Weighted inner inverse for rectangular matrices ⋮ A note on clean elements and inverses along an element ⋮ The one-sided inverse along an element in semigroups and rings ⋮ Existence and Representations of Solutions to Some Constrained Systems of Matrix Equations ⋮ The polarity along an element in rings ⋮ Outer inverses in semigroups belonging to the prescribed Green's equivalence classes ⋮ One-sided w-core inverses in rings with an involution ⋮ Characterizations and representations of the inverse along an element ⋮ One-sided weighted outer inverses of tensors ⋮ Further results on the (b, c)-inverse, the outer inverse AT,S(2) and the Moore–Penrose inverse in the Banach context ⋮ Centralizer's applications to the inverse along an element ⋮ Weighted Moore-Penrose inverses and weighted core inverses in rings with involution ⋮ Centralizer's applications to the \((b, c)\)-inverses in rings ⋮ One-sided (b,c)-inverses in rings

Cites Work

• On generalized inverses and Green's relations
• A note on Drazin inverses
• The inverse along a lower triangular matrix
• Further results on the inverse along an element in semigroups and rings
• Generalized inverses modulo ℋ in semigroups and rings
• Outer generalized inverses with prescribed ideals

This page was built for publication: The inverse along an element in rings with an involution, Banach algebras and -algebras